In Olber's paradox, the 2 most important assumptions made were

1) The Universe is infinite.

2) The Universe is static and infinitely old.

References to what is now known as Olbers' Paradox date back to the 1500s. This paradox has come up periodically in history. In 1929, Edwin Hubble discovered that the universe is expanding, which offers an explanation to the paradox. Prior to this, any hypotheses were quickly dismissed.

As there are thousands of stars to light up our universe, the question that Heinrich Wilhelm Olbers asked was "Why is the sky dark at night?"

Yes - the night sky would be yellow-white (Olbers' Paradox)

Because the universe is neither infinitely large nor infinitely old. If you need more details, look up "Olbers' paradox".